Interpolation with function parameter and UMD spaces.
A (real or complex) Banach space E is said to have the unconditionaly property for martingale differences (UMD-property, for short) if E-values martingale differences are unconditional in L(E;[0,1]). The main reason for the interest in this new class of spaces is that the analogues of several classical results on martingales and singular integrals are also true for a Banach space belonging to this class.